The geometry of sedenion zero divisors

Abstract: The sedenion algebra is a non-associative real algebra obtained from the octonions via the Cayley-Dickson construction. Its zero divisors admit a natural description as a principal bundle over the Stiefel manifold $V_{2,7}$, with total space the compact Lie group $G_2$ and fiber $S^3$, which is similar to the Hopf fibration.

In this talk, we discuss some geometric aspects of this fibration. We show that the natural submanifold metric on the total space is isometric to a naturally reductive left-invariant metric on $G_2$, yielding a Riemannian submersion onto an exceptional symmetric space. We also consider a deformation of the metric on $V_{2,7}$, analogous to the Berger spheres, obtaining a new Einstein metric and a family of non-negatively curved metrics.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Differential geometry.

The seminar meets every other Wednesday. To accommodate most time zones, the time rotates. The Zoom link is sent to the mailing list around 24 hours before each talk. To subscribe to the mailing list, fill the following form: docs.google.com/forms/d/e/1FAIpQLSdKrJ-nivgjr7ZVJmIY0qkN-VbzTl5NHHNyg6nNsCqjhB-4WA/viewform?usp=sf_link.

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